A lemma on C ₀-semigroups on time scales and approximate controllability of the heat dynamic equation

Abstract

In this paper, we present a lemma that allows us to characterize a broad class of C ₀-semigroups on time scales, which can be applied to prove existence and uniqueness of solutions of systems of partial differential equations where the time domain is a time scale. The result obtained is applied to study the controllability of the heat equation on time scales. The lemma presented in this paper can be seen as a unification of the one proved by H. Leiva in [28], for semigroups in [0,∞).